You said Outlook clients go offline, do you mean mail flow stops or mailbox cannot be accessed?
When you rebooting the mail server, please check if the database that was activated on mail server is mounted on the second server.
If yes, login to OWA and test if you can open those mailbox (of the database that was activated on mail server)
If you mean mail flow stops, did you get any NDR message?
Can you see the message in Sent Items? When searching message tracking log, any event info?
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